Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908789045723136 |
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| author | Mai, Peizhi Zhao, Jinchao Tenkila, Gaurav Hackner, Nico A. Kush, Dhruv Pan, Derek Phillips, Philip W. |
| author_facet | Mai, Peizhi Zhao, Jinchao Tenkila, Gaurav Hackner, Nico A. Kush, Dhruv Pan, Derek Phillips, Philip W. |
| contents | The Hubbard model is a standard theoretical tool for studying materials with strong electron-electron interactions, such as the cuprate superconductors. Unfortunately, interaction-driven phenomena such as the transition into the strongly correlated Mott insulator phase are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai-Kohmoto model displays similar Mott physics. Here we show how the Hatsugai-Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically re-introduce all the momentum mixing the original Hatsugai-Kohmoto model omits. This can be accomplished by grouping $n$-momenta into a cell and hybridizing them resulting in the momentum-mixing Hatsugai-Kohmoto (MMHK) model. We recover the Bethe ansatz ground state energy of the one-dimensional Hubbard model to within 1$\%$ from only ten mixed momenta. Overall the convergence scales as $1/n^2$ as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe the MMHK model offers an alternative tool for strongly correlated quantum matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model Mai, Peizhi Zhao, Jinchao Tenkila, Gaurav Hackner, Nico A. Kush, Dhruv Pan, Derek Phillips, Philip W. Strongly Correlated Electrons Superconductivity The Hubbard model is a standard theoretical tool for studying materials with strong electron-electron interactions, such as the cuprate superconductors. Unfortunately, interaction-driven phenomena such as the transition into the strongly correlated Mott insulator phase are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai-Kohmoto model displays similar Mott physics. Here we show how the Hatsugai-Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically re-introduce all the momentum mixing the original Hatsugai-Kohmoto model omits. This can be accomplished by grouping $n$-momenta into a cell and hybridizing them resulting in the momentum-mixing Hatsugai-Kohmoto (MMHK) model. We recover the Bethe ansatz ground state energy of the one-dimensional Hubbard model to within 1$\%$ from only ten mixed momenta. Overall the convergence scales as $1/n^2$ as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe the MMHK model offers an alternative tool for strongly correlated quantum matter. |
| title | Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2401.08746 |